Final answer:
Using Avogadro's law, the final volume of the gas after adding 0.15 mole to the initial 0.30 mole in a constant temperature and pressure environment is calculated to be 3.75 liters.
Step-by-step explanation:
To determine the final volume of the gas when additional moles are added, we can use the ideal gas law in the form of Avogadro's law, which states that at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of the gas. In this case, temperature and pressure are constant, so we can set up a proportion based on the initial conditions and the conditions after more gas is added:
V1/n1 = V2/n2
Where V1 is the initial volume (2.5 liters), n1 is the initial number of moles (0.30 mol), V2 is the final volume, and n2 is the final number of moles (0.30 mol + 0.15 mol = 0.45 mol).
Substituting the known values into the equation:
2.5 L / 0.30 mol = V2 / 0.45 mol
Solving for V2 gives:
V2 = (2.5 L * 0.45 mol) / 0.30 mol
V2 = 3.75 liters
Therefore, the final volume of the gas after adding 0.15 mole is 3.75 liters.